Mathematical Research Letters

Volume 15 (2008)

Number 5

Bihermitian metrics on Hopf surfaces

Pages: 827 – 839

DOI: http://dx.doi.org/10.4310/MRL.2008.v15.n5.a1

Authors

Vestislav Apostolov (Université du Québec à Montréal)

Georges Dloussky (Université dÕAix-Marseille)

Abstract

Inspired by a construction due to Hitchin~\cite{hitchin4}, we produce strongly bihermitian metrics on certain Hopf complex surfaces, which integrate the locally conformally Kähler metrics found by Gauduchon–Ornea~\cite{GO}. We also show that the Inoue complex surfaces with $b_2=0$ do not admit bihermitian metrics. This completes the classification of the compact complex surfaces admitting strongly bihermitian metrics.

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